On the Force Capabilities of Two-Degree-of-Freedom Planar Parallel Mechanisms Equipped With Torque Limiters

2013 ◽  
Author(s):  
Wei Chen ◽  
Clément Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Joint Torque ◽  
Design Stage ◽  
Parallel Mechanisms ◽  
Human Beings ◽  
Safety Index ◽  
End Effector ◽  
Two Degree Of Freedom ◽  
Insight Into

Safety is the most important issue that should be considered when designing collaborative robots that are intended to physically interact with humans. This paper investigates the force capabilities of two-degree-of-freedom planar parallel mechanisms that are equipped with torque limiters (safety clutches). Joint torque limiting devices are used in these mechanisms in order to limit the forces that the robot can apply to its environment. Such devices aim at ensuring the safety of the human beings interacting with the robot. However, because the torque-limiting devices are mounted at the joints of the robot, the end-effector force capabilities induced by these devices are dependent on the pose (Jacobian matrix) of the robot. Therefore, the characteristics of the torque limiting devices must be determined at the design stage in order to ensure safety and maximize effectiveness in all possible poses of the robot. Two types of planar two-degree-of-freedom parallel mechanisms are considered in this paper. Their architecture is first described. Then, the force capabilities are studied based on the Jacobian matrices. The maximum force that can be applied at the end-effector for given torque limits (safety index) is determined together with the maximum isotropic force (effectiveness) that can be produced. The ratio between these two forces, referred to as the force efficiency, can be considered as a performance index. Finally, some numerical results are proposed which can provide insight into the design of cooperation robots based on parallel architectures.

Force Capabilities of Two-Degree-of-Freedom Serial Robots Equipped With Passive Isotropic Force Limiters

2015 ◽  
Author(s):  
Meiying Zhang ◽  
Thierry Laliberté ◽  
Clément Gosselin
Keyword(s):  
Human Robot Interaction ◽  
Contact Forces ◽  
Degree Of Freedom ◽  
Practical Implementation ◽  
Robot Interaction ◽  
End Effector ◽  
Serial Robots ◽  
Serial Robot ◽  
Maximum Contact ◽  
Two Degree Of Freedom

This paper proposes the use of passive force and torque limiting devices to bound the maximum forces that can be applied at the end-effector or along the links of a robot, thereby ensuring the safety of human-robot interaction. Planar isotropic force limiting modules are proposed and used to analyze the force capabilities of a two-degree-of-freedom planar serial robot. The force capabilities at the end-effector are first analyzed. It is shown that, using isotropic force limiting modules, the performance to safety index remains excellent for all configurations of the robot. The maximum contact forces along the links of the robot are then analyzed. Force and torque limiters are distributed along the structure of the robot in order to ensure that the forces applied at any point of contact along the links are bounded. A power analysis is then presented in order to support the results. Finally, examples of mechanical designs of force/torque limiters are shown to illustrate a possible practical implementation of the concept.

Seven-Position Synthesis of a Spatial Eight-Bar Linkage by Constraining a TRS Serial Chain

2009 ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Degree Of Freedom ◽  
Upper Arm ◽  
End Effector ◽  
Serial Chain ◽  
Position Synthesis ◽  
Two Degree Of Freedom ◽  
Puma Robot

In this paper, we use seven-position synthesis to add four TS constraints to a TRS serial chain robot and obtain a two degree-of-freedom spatial eight-bar linkage. The TRS chain is an elbow manipulator, similar to a PUMA robot. We synthesize a TS dyad to connect the base of the robot to its forearm, and then we synthesize three TS dyads that connect the upper arm of the robot to its end-effector. The result is a two degree-of-freedom spatial eight-bar linkage that moves through seven prescribed positions. It consists of a TRST loop supporting a 3TS-RS platform, which we denote as a TS-TRS-3TS spatial linkage. We formulate and solve the design equations for the TS dyads, and analyze the resulting eight-bar linkage. An example demonstrates our results.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

The Workspace of a General Geometry Planar Three-Degree-of-Freedom Platform-Type Manipulator

1993 ◽  
Vol 115 (2) ◽  
pp. 269-276 ◽  
Author(s):  
G. R. Pennock ◽  
D. J. Kassner
Keyword(s):  
Degree Of Freedom ◽  
Arbitrary Orientation ◽  
End Effector ◽  
The Absolute ◽  
Position Problem ◽  
General Geometry ◽  
Three Degree Of Freedom ◽  
Insight Into

This paper focuses on the direct workspace problems of a general geometry fully-parallel-actuated, planar three-degree-of-freedom platform-type manipulator. A set of equations are presented that determine the workspace as a function of the platform orientation. The formulation is governed by the solution to the inverse position problem of the manipulator. The reachable positions of the end-effector point, for a specified platform orientation, are analyzed. To illustrate the concepts, a practical example is included where the end-effector is required to move a cup filled with water. Then the platform orientation, for a specified location of the end-effector point, is studied. If an arbitrary orientation is possible, the specified location of the end-effector point is said to be within the primary workspace. The paper includes a detailed discussion of the total primary workspaces of the manipulator. The approach adopted here is to regard the manipulator as a combination of three planar, three-revolute open chains. For the sake of completeness, the influence of special manipulator geometry on the workspace is also discussed. Finally, the paper includes the conditions that cause stationary configurations of the manipulator. Insight into these undesirable configurations is provided by a study of the location of the absolute instant center of the platform.

Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

2006 ◽  
Vol 129 (4) ◽  
pp. 390-396 ◽  
Author(s):  
Si J. Zhu ◽  
Zhen Huang ◽  
Hua F. Ding
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Rear Part ◽  
Lower Mobility ◽  
Acceleration Analysis

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N<6) mechanism, this method can build a square (N×N) Jacobian matrix and cubic (N×N×N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

Reactionless Two-Degree-of-Freedom Planar Parallel Mechanism With Variable Payload

2009 ◽  
Author(s):  
Alexandre Lecours ◽  
Cle´ment Gosselin
Keyword(s):  
Dynamic Simulation ◽  
Parallel Mechanism ◽  
Reaction Force ◽  
Simulation Software ◽  
Degree Of Freedom ◽  
Dynamic Balancing ◽  
End Effector ◽  
Planar Mechanism ◽  
Two Degree Of Freedom ◽  
Arbitrary Trajectory

A reactionless mechanism is one which does not exert any reaction force or moment on its base at all times, for any arbitrary trajectory of the mechanism. This paper addresses the static and dynamic balancing of a two-degree-of-freedom parallel planar mechanism (five-bar mechanism). A simple and effective adaptive balancing method is presented that allows the mechanism to maintain the reactionless condition for a range of payloads. Important proofs concerning the balancing of five-bar mechanisms are also presented. The design of a real mechanism where parallelogram linkages are used to produce pure translations at the end-effector is also presented. Finally, using dynamic simulation software, it is shown that the mechanism is reactionless for arbitrarily chosen trajectories and for a variety of payloads.

A Quasi-Static Model for Planar Compliant Parallel Mechanisms

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Cyril Quennouelle ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanism ◽  
Applied Load ◽  
Jacobian Matrix ◽  
Static Model ◽  
Parallel Mechanisms ◽  
Compliance Matrix ◽  
End Effector ◽  
Kinematic Constraints ◽  
Compliant Parallel Mechanism ◽  
External Loads

In this paper, the mobility, the kinematic constraints, the pose of the end-effector, and the static constraints that lead to the kinematostatic model of a compliant parallel mechanism are introduced. A formulation is then provided for its instantaneous variation—the quasi-static model. This new model allows the calculation of the variation in the pose as a linear function of the motion of the actuators and the variation in the external loads through two new matrices: the compliant Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism. Finally, a simple application to a planar four-bar mechanism is presented to illustrate the use of this model and the new possibilities that it opens, notably the study of the kinematics for any range of applied load.

Force Capabilities of Two-Degree-of-Freedom Serial Robots Equipped With Passive Isotropic Force Limiters

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Meiying Zhang ◽  
Thierry Laliberté ◽  
Clément Gosselin
Keyword(s):  
Human Robot Interaction ◽  
Contact Forces ◽  
Degree Of Freedom ◽  
Practical Implementation ◽  
Robot Interaction ◽  
End Effector ◽  
Serial Robots ◽  
Serial Robot ◽  
Maximum Contact ◽  
Two Degree Of Freedom

This paper proposes the use of passive force and torque limiting devices to bound the maximum forces that can be applied at the end-effector or along the links of a robot, thereby ensuring the safety of human–robot interaction. Planar isotropic force limiting modules are proposed and used to analyze the force capabilities of a two-degree-of-freedom (2DOF) planar serial robot. The force capabilities at the end-effector are first analyzed. It is shown that, using isotropic force limiting modules, the performance to safety index remains excellent for all configurations of the robot. The maximum contact forces along the links of the robot are then analyzed. Force and torque limiters are distributed along the structure of the robot in order to ensure that the forces applied at any point of contact along the links are bounded. A power analysis is then presented in order to support the results. Finally, examples of mechanical designs of force/torque limiters are shown to illustrate a possible practical implementation of the concept.

Analytical Computation of the Actuator and Cartesian Workspace Boundaries for a Planar 2-Degree-of-Freedom Translational Tensegrity Mechanism

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Samuel Chen ◽  
Marc Arsenault
Keyword(s):  
Translational Motion ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
End Effector ◽  
Optimal Mechanism ◽  
High Acceleration ◽  
Pick And Place ◽  
Actuation Scheme ◽  
Two Degree Of Freedom ◽  
Robotic Applications

Tensegrity mechanisms are interesting candidates for high-acceleration robotic applications since their use of cables allows for a reduction in the weight and inertia of their mobile parts. In this work, a planar two-degree-of-freedom translational tensegrity mechanism that could be used for pick and place applications is introduced. The mechanism uses a strategic actuation scheme to generate the translational motion as well as to ensure that the cables remain taut at all times. Analytical solutions to the direct and inverse kinematic problems are developed, and the mechanism’s workspace boundaries are computed in both the actuator and Cartesian spaces. The influence of the mechanism’s geometry on the size and shape of the Cartesian workspace are then studied. Based on workspace size only, it is found that the optimal mechanism geometry corresponds to a relatively large ratio between the length of the struts and the width of the base and end-effector.

The relationship between controlled joint torque and end-effector force in underactuated robotic systems

Robotica ◽  
2010 ◽  
Vol 29 (4) ◽  
pp. 581-584 ◽  
Author(s):  
Jaeheung Park
Keyword(s):  
Jacobian Matrix ◽  
Joint Torque ◽  
Generalized Jacobian ◽  
End Effector ◽  
Joint Torques ◽  
Floating Base ◽  
Force Moment ◽  
Generalized Jacobian Matrix ◽  
The Relationship ◽  
Jacobian Inverse

SUMMARYThe generalized Jacobian matrix was introduced for dealing with end-effector control in space robots. One of the applications of this Jacobian is to be used in Jacobian transpose control to generate joint torques given end-effector position error. It would be misleading, however, to consider the transpose of this Jacobian as a mapping from end-effector force/moment to controlled joint torques for underactuated systems or floating base robots. This paper explains why it does not represent the mapping and provides a simple example. Later, the correct mapping is provided using the dynamically consistent Jacobian inverse and then a method to compute the actuated-joint torques is explained given the desired end-effector force. Finally, the effect of using the generalized Jacobian in the Jacobian transpose control is analyzed.

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